Modelling the Temperature Dependent Biaxial Response of Poly(ether-ether-ketone) Above and Below the Glass Transition for Thermoforming Applications

Abstract

Desire to accurately predict the deformation behaviour throughout industrial forming processes, such as thermoforming and stretch blow moulding, has led to the development of mathematical models of material behaviour, with the ultimate aim of embedding into forming simulations enabling process and product optimization. Through the use of modern material characterisation techniques, biaxial data obtained at conditions comparable to the thermoforming process was used to calibrate the Buckley material model to the observed non-linear viscoelastic stress/strain behaviour. The material model was modified to account for the inherent anisotropy observed between the principal directions through the inclusion of a Holazapfel–Gasser–Ogden hyperelastic element. Variations in the post-yield drop in stress values associated with deformation rate and specimen temperature below the glass transition were observable, and facilitated in the modified model through time-temperature superposition creating a linear relationship capable of accurately modelling this change in yield stress behaviour. The modelling of the region of observed flow stress noted when above the glass transition temperature was also facilitated through adoption of the same principal. Comparison of the material model prediction was in excellent agreement with experiments at strain rates and temperatures of 1–16 s−1 and 130–155 °C respectively, for equal-biaxial mode of deformation. Temperature dependency of the material model was well replicated with across the broad temperature range in principal directions, at the reference strain rate of 1 s−1. When concerning larger rates of deformation, minimum and maximum average error levels of 6.20% and 10.77% were noted. The formulation, and appropriate characterization, of the modified Buckley material model allows for a stable basis in which future implementation into representative forming simulations of poly-aryl-ether-ketones, poly(ether-ether-ketone) (PEEK) and many other post-yield anisotropic polymers.

Constitutive Modelling of Polylactic Acid at Large Deformation Using Multiaxial Strains

“…In particular, V 2 s , the shear activation volume in arm 2, is assigned to be a function of the plastic strain in the Eyring process in arm 2. The appropriate measure of strain is the scalar octahedral plastic strain e p given by: (28) For the functional form of the evolution of the activation volume, we have adapted the approach used by Turner et al [26] for the evolution of the fictive temperature. Then:…”

Thermo-Mechanical Behavior of Poly(ether ether ketone): Experiments and Modeling

“…Results of DMA analysis in the temperature-sweep mode are presented in [ 9 , 10 , 11 , 12 , 13 , 14 ]. Observations in tests with various strain rates are reported in [ 10 , 15 , 16 , 17 , 18 , 19 ] for tensile deformation, in [ 10 , 20 , 21 , 22 ] for compressive deformation, and in [ 23 , 24 ] for biaxial loading. Experimental data in cyclic and fatigue tests are presented in [ 10 , 14 , 25 , 26 , 27 , 28 , 29 ].…”

“…As PEEK is a semicrystalline polymer, its time- and rate-dependent behavior can be described by conventional models in viscoelasticity and viscoplasticity of semicrystalline polymers, see [ 41 , 42 , 43 ], to mention a few. Constitutive equations accounting for the peculiarities in the thermo–mechanical response of PEEK induced by stiffness of its backbone chains were developed in [ 18 , 19 , 22 , 24 , 29 , 44 , 45 , 46 ].…”

“…Previous studies on the thermo–mechanical behavior of PEEK focused on its viscoelastic and viscoplastic responses below the glass transition temperature °C [ 24 , 29 , 44 , 45 , 46 ]. Above this temperature, only observations in tensile tests with constant strain rates were reported and analyzed in [ 18 , 19 , 22 ].…”

“…Unlike previous studies on modeling the time- and rate-dependent behavior of PEEK subjected to arbitrary 3D deformations with finite strains [ 19 , 24 , 29 , 44 , 46 ], we confine ourselves to the analysis of its thermo-mechanical response under uniaxial deformation with small strains. This allows the number of adjustable coefficients in the constitutive equations to be reduced noticeably (compared with conventional models).…”